TY - JOUR
T1 - Rao's score, Neyman's C(α) and Silvey's LM tests
T2 - An essay on historical developments and some new results
AU - Bera, Anil K.
AU - Bilias, Yannis
N1 - Funding Information:
We are grateful to two referees for many helpful suggestions, and to C.R. Rao, B. Li, F. Cribari-Neto, S. Ramamoorti and D. Majumdar for comments on an earlier version of the paper. We would also like to thank Naoko Miki, Janet Fitch, Armen Hovsepian, Yulia Kotlyarova, Gamini Premaratne, Sue Streeter and Robert Rozovsky for their help in preparing the manuscript. However, we retain the responsibility for any remaining errors. A part of this work was done during a visit by the first author to the Department of Economics, Iowa State University, whose financial support is gratefully acknowledged.
PY - 2001/8/1
Y1 - 2001/8/1
N2 - Rao's (Proc. Cambridge Philos. Soc. 44 (1948a) 50) seminal paper introduced a fundamental principle of testing based on the score function as an alternative to likelihood ratio and Wald tests. Neyman's (In: Grenander, (Ed.), Probability and Statistics, the Harald Cramér Volume, Almqvist and Wiksell, Uppsala, pp. 213-234) approach, in view of the presence of nuisance parameters, emphasized the generality and attractive features of the score-based tests. Silvey (Ann. Math. Statist. 30 (1959) 389) rediscovered the score test as a Lagrange multiplier test. Breusch and Pagan's (Rev. Econom. Stud. 47 (1980) 239) exposition of the score test in a general framework in the context of econometric modeling resulted in an increased activity on specification testing in econometrics. In this paper we trace these historical developments emphasizing the optimality features of tests based on scores and their usefulness in practical problems in statistics and econometrics. In so doing we give some new results, present easier computation of score-based tests and alternative derivations of some known results. We also discuss a connection between Rao's score test and the seemingly unrelated literature of Fisher's discriminant function, Mahalanobis' D2 and Hotelling's T2.
AB - Rao's (Proc. Cambridge Philos. Soc. 44 (1948a) 50) seminal paper introduced a fundamental principle of testing based on the score function as an alternative to likelihood ratio and Wald tests. Neyman's (In: Grenander, (Ed.), Probability and Statistics, the Harald Cramér Volume, Almqvist and Wiksell, Uppsala, pp. 213-234) approach, in view of the presence of nuisance parameters, emphasized the generality and attractive features of the score-based tests. Silvey (Ann. Math. Statist. 30 (1959) 389) rediscovered the score test as a Lagrange multiplier test. Breusch and Pagan's (Rev. Econom. Stud. 47 (1980) 239) exposition of the score test in a general framework in the context of econometric modeling resulted in an increased activity on specification testing in econometrics. In this paper we trace these historical developments emphasizing the optimality features of tests based on scores and their usefulness in practical problems in statistics and econometrics. In so doing we give some new results, present easier computation of score-based tests and alternative derivations of some known results. We also discuss a connection between Rao's score test and the seemingly unrelated literature of Fisher's discriminant function, Mahalanobis' D2 and Hotelling's T2.
KW - 62F03
KW - 62J20
KW - 62P20
KW - LM test
KW - Neyman's C(α) test
KW - Rao's score test
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U2 - 10.1016/S0378-3758(00)00343-8
DO - 10.1016/S0378-3758(00)00343-8
M3 - Article
AN - SCOPUS:0009607846
SN - 0378-3758
VL - 97
SP - 9
EP - 44
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 1
ER -